# [R] implementation of Prentice method in cch()

From: Jin Wang <jinwang25_at_gmail.com>
Date: Tue, 15 Jul 2008 19:58:07 -0400

Case cohort function cch() is in survival package. In cch(), the prentice method is implemented like this:

Prentice <- function(tenter, texit, cc, id, X, ntot,robust){

eps <- 0.00000001
cens <- as.numeric(cc>0) # Censorship indicators     subcoh <- as.numeric(cc<2) # Subcohort indicators
## Calculate Prentice estimate

ent2 <- tenter
ent2[cc==2] <- texit[cc==2]-eps
fit1 <- coxph(Surv(ent2,texit,cens)~X,eps=eps,x=TRUE)
## Calculate Prentice estimate and variance
nd <- sum(cens) # Number of failures

```    nc <- sum(subcoh) # Number in subcohort
ncd <- sum(cc==1) #Number of failures in subcohort
X <- as.matrix(X)
```

aent <- c(tenter[cc>0],tenter[cc<2])     aexit <- c(texit[cc>0],texit[cc<2])
aX <- rbind(as.matrix(X[cc>0,]),as.matrix(X[cc<2,]))
```    aid <- c(id[cc>0],id[cc<2])
dum <- rep(-100,nd)
dum <- c(dum,rep(0,nc))
```

gp <- rep(1,nd)
gp <- c(gp,rep(0,nc))
fit <-
coxph(Surv(aent,aexit,gp)~aX+offset(dum)+cluster(aid),eps=eps,x=TRUE,
```                 iter.max=35,init=fit1\$coefficients)
db <- resid(fit,type="dfbeta")
```

db <- as.matrix(db)
db <- db[gp==0,]
```    fit\$phase2var<-(1-(nc/ntot))*t(db)%*%(db)
fit\$naive.var <- fit\$naive.var+fit\$phase2var
fit\$var<-fit\$naive.var

```

fit\$coefficients <- fit\$coef <- fit1\$coefficients     fit
}

The first fit1<-coxph() estimate the coefficient and second fit<-coxph() which seems a SelfPrentice method to estimate the variance. My question is why second coxph() estimate Prentice variance using SelfPrentice method. Should the jacknife variance of Prentice be implemented like: fit1 <- coxph(Surv(ent2,texit,cens)~X+cluster(id),eps=eps,x=TRUE) Th other question is unique id is not necessary in whole program, Can we just allow multiple ids without affecting the final result?

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